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Which number is closest to $\sqrt{67}$ ? $\newline$ Choices: $\newline$ (A) $8.1$ $\newline$ (B) $8.8$ $\newline$ (C) $9.1$ $\newline$ (D) $8.7$

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Estimate positive square roots

Full solution

Q. Which number is closest to

\sqrt{67}

?

\newline

Choices:

\newline

(A)

8.1

\newline

(B)

8.8

\newline

(C)

9.1

\newline

(D)

8.7

Calculate Square Root: Step $1$ : Calculate the square root of $67$ using a calculator. $\newline$ Calculation: $\sqrt{67} \approx 8.185$ .
Compare Calculated Value: Step $2$ : Compare the calculated square root with the given choices. $\newline$ Choices are $8.1$ , $8.8$ , $8.7$ , and $9.1$ . $\newline$ $8.185$ is closest to $8.1$ and $8.2$ , but since $8.2$ isn't an option, we compare with $8.1$ and $8.7$ .
Determine Numerical Closeness: Step $3$ : Determine which choice is numerically closer to $8.185$ . Difference with $8.1 = 8.185 - 8.1 = 0.085$ . Difference with $8.7 = 8.7 - 8.185 = 0.515$ . $8.1$ is closer to $8.185$ than $8.7$ .

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